bitwidths

Bitwidth is the number of bits used to represent a value in a given context, and it influences the range, precision, and storage cost of that value. It applies to integers, floating-point numbers, and other binary encodings, and can be fixed by a language or hardware architecture or vary with the program’s data types.

Common fixed bitwidths include 8, 16, 32, and 64 bits. These widths appear in integers and pointers on many platforms, and language standards provide fixed-width types such as 8-, 16-, 32-, and 64-bit variants. In practice, the chosen bitwidth affects how many distinct values can be represented and how arithmetic handles overflow.

For integers, unsigned and signed representations differ. With n bits, unsigned integers span 0 to 2^n − 1. Signed integers typically use two’s complement, spanning −2^(n−1) to 2^(n−1) − 1. Overflow behavior depends on representation and operation, and can lead to wraparound or exceptions.

Floating-point numbers use bitwidths that encode sign, exponent, and mantissa. Common widths are 32-bit (single precision) and 64-bit (double precision), with emerging 16-bit (half) and wider formats for specialized applications. Floating-point bitwidths determine dynamic range and precision and are governed by standards such as IEEE 754.

Bitwidths also affect performance and portability. They influence memory usage, alignment, and the interface between software and hardware, including vector units with wide registers (e.g., 128- or 256-bit lanes). Some languages permit custom or arbitrary-precision representations, trading speed for precision. In short, bitwidths are a foundational concept shaping data representation and computation.